Problem: Simplify the following expression: $\dfrac{110q^4}{132q^5}$ You can assume $q \neq 0$.
Solution: $ \dfrac{110q^4}{132q^5} = \dfrac{110}{132} \cdot \dfrac{q^4}{q^5} $ To simplify $\frac{110}{132}$ , find the greatest common factor (GCD) of $110$ and $132$ $110 = 2 \cdot 5 \cdot 11$ $132 = 2 \cdot 2 \cdot 3 \cdot 11$ $ \mbox{GCD}(110, 132) = 2 \cdot 11 = 22 $ $ \dfrac{110}{132} \cdot \dfrac{q^4}{q^5} = \dfrac{22 \cdot 5}{22 \cdot 6} \cdot \dfrac{q^4}{q^5} $ $\phantom{ \dfrac{110}{132} \cdot \dfrac{4}{5}} = \dfrac{5}{6} \cdot \dfrac{q^4}{q^5} $ $ \dfrac{q^4}{q^5} = \dfrac{q \cdot q \cdot q \cdot q}{q \cdot q \cdot q \cdot q \cdot q} = \dfrac{1}{q} $ $ \dfrac{5}{6} \cdot \dfrac{1}{q} = \dfrac{5}{6q} $